Real
StressDivergence::computeQpJacobian()
{
Real sum_C3x3 = _Jacobian_mult[_qp].sum_3x3();
RealGradient sum_C3x1 = _Jacobian_mult[_qp].sum_3x1();
Real jacobian = 0.0;
// B^T_i * C * B_j
jacobian += _Jacobian_mult[_qp].stiffness(
_component, _component, _grad_test[_i][_qp], _grad_phi[_j][_qp]); // B^T_i * C *B_j
if (_volumetric_locking_correction)
{
// jacobian = Bbar^T_i * C * Bbar_j where Bbar = B + Bvol
// jacobian = B^T_i * C * B_j + Bvol^T_i * C * Bvol_j + Bvol^T_i * C * B_j + B^T_i * C * Bvol_j
// Bvol^T_i * C * Bvol_j
jacobian += sum_C3x3 * (_avg_grad_test[_i][_component] - _grad_test[_i][_qp](_component)) *
(_avg_grad_phi[_j][_component] - _grad_phi[_j][_qp](_component)) / 9.0;
// B^T_i * C * Bvol_j
jacobian += sum_C3x1(_component) * _grad_test[_i][_qp](_component) *
(_avg_grad_phi[_j][_component] - _grad_phi[_j][_qp](_component)) / 3.0;
// Bvol^T_i * C * B_j
SymmTensor phi;
if (_component == 0)
{
phi.xx() = _grad_phi[_j][_qp](0);
phi.xy() = _grad_phi[_j][_qp](1);
phi.xz() = _grad_phi[_j][_qp](2);
}
else if (_component == 1)
{
phi.yy() = _grad_phi[_j][_qp](1);
phi.xy() = _grad_phi[_j][_qp](0);
phi.yz() = _grad_phi[_j][_qp](2);
}
else if (_component == 2)
{
phi.zz() = _grad_phi[_j][_qp](2);
phi.xz() = _grad_phi[_j][_qp](0);
phi.yz() = _grad_phi[_j][_qp](1);
}
SymmTensor tmp(_Jacobian_mult[_qp] * phi);
jacobian += (tmp.xx() + tmp.yy() + tmp.zz()) *
(_avg_grad_test[_i][_component] - _grad_test[_i][_qp](_component)) / 3.0;
}
if (_dt > 0)
return jacobian * (1 + _alpha + _zeta / _dt);
else
return jacobian;
}
ColumnMajorMatrix
CrackFrontDefinition::rotateToCrackFrontCoords(const SymmTensor tensor, const unsigned int node_index) const
{
ColumnMajorMatrix tensor_CMM;
tensor_CMM(0,0) = tensor.xx();
tensor_CMM(0,1) = tensor.xy();
tensor_CMM(0,2) = tensor.xz();
tensor_CMM(1,0) = tensor.xy();
tensor_CMM(1,1) = tensor.yy();
tensor_CMM(1,2) = tensor.yz();
tensor_CMM(2,0) = tensor.xz();
tensor_CMM(2,1) = tensor.yz();
tensor_CMM(2,2) = tensor.zz();
ColumnMajorMatrix tmp = _rot_matrix[node_index] * tensor_CMM;
ColumnMajorMatrix rotT = _rot_matrix[node_index].transpose();
ColumnMajorMatrix rotated_tensor = tmp * rotT;
return rotated_tensor;
}
Real
StressDivergence::computeQpOffDiagJacobian(unsigned int jvar)
{
unsigned int coupled_component = 0;
bool active = false;
if (_xdisp_coupled && jvar == _xdisp_var)
{
coupled_component = 0;
active = true;
}
else if (_ydisp_coupled && jvar == _ydisp_var)
{
coupled_component = 1;
active = true;
}
else if (_zdisp_coupled && jvar == _zdisp_var)
{
coupled_component = 2;
active = true;
}
if (active)
{
Real sum_C3x3 = _Jacobian_mult[_qp].sum_3x3();
RealGradient sum_C3x1 = _Jacobian_mult[_qp].sum_3x1();
Real jacobian = 0.0;
jacobian += _Jacobian_mult[_qp].stiffness(
_component, coupled_component, _grad_test[_i][_qp], _grad_phi[_j][_qp]); // B^T_i * C *B_j
if (_volumetric_locking_correction)
{
// jacobian = Bbar^T_i * C * Bbar_j where Bbar = B + Bvol
// jacobian = B^T_i * C * B_j + Bvol^T_i * C * Bvol_j + Bvol^T_i * C * B_j + B^T_i * C *
// Bvol_j
// Bvol^T_i * C * Bvol_j
jacobian += sum_C3x3 * (_avg_grad_test[_i][_component] - _grad_test[_i][_qp](_component)) *
(_avg_grad_phi[_j][coupled_component] - _grad_phi[_j][_qp](coupled_component)) /
9.0;
// B^T_i * C * Bvol_j
jacobian += sum_C3x1(_component) * _grad_test[_i][_qp](_component) *
(_avg_grad_phi[_j][coupled_component] - _grad_phi[_j][_qp](coupled_component)) /
3.0;
// Bvol^T_i * C * B_i
SymmTensor phi;
if (coupled_component == 0)
{
phi.xx() = _grad_phi[_j][_qp](0);
phi.xy() = _grad_phi[_j][_qp](1);
phi.xz() = _grad_phi[_j][_qp](2);
}
else if (coupled_component == 1)
{
phi.yy() = _grad_phi[_j][_qp](1);
phi.xy() = _grad_phi[_j][_qp](0);
phi.yz() = _grad_phi[_j][_qp](2);
}
else if (coupled_component == 2)
{
phi.zz() = _grad_phi[_j][_qp](2);
phi.xz() = _grad_phi[_j][_qp](0);
phi.yz() = _grad_phi[_j][_qp](1);
}
SymmTensor tmp(_Jacobian_mult[_qp] * phi);
jacobian += (tmp.xx() + tmp.yy() + tmp.zz()) *
(_avg_grad_test[_i][_component] - _grad_test[_i][_qp](_component)) / 3.0;
}
if (_dt > 0)
return jacobian * (1 + _alpha + _zeta / _dt);
else
return jacobian;
}
if (_temp_coupled && jvar == _temp_var)
return _d_stress_dT[_qp].rowDot(_component, _grad_test[_i][_qp]) * _phi[_j][_qp];
return 0;
}